MATH 10A Lecture 12: Math 10A 1-25 Lecture - Limits
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Principle: limits interact nicely with addition, subtraction, multiplication, division, exponents, logarithms, and trig functions. In detail: (x2 5)=32 5=4 lim x 3 x2 lim x 3. 5 lim x 3 lim x 3 (x2 5)=lim x 3. 0 is indeterminate. a hole at x = 1, but otherwise looks the same as (5x-2) (x+1) |a| = { a if a 0, Example: lim x 2 lim x 1 lim x 1 lim x 1 lim x 4. Dne (5x2-7x+2) (x2-1) (5x-2)(x-1) (x+1)(x-1) lim x 4 lim x 4 lim x 4. Its height (in feet) after t seconds is given by the following function: f(t) = -16t2 + 144 f(0) = 144 = bridge height a)average velocity between t=2 and 3? t=2 and t=3 . The stone is falling at 80 ft/sec, on average between: average velocity between t=2 and t=2. 5 f (2. 5) f (2) 72 ft /sec: average velocity between t=2 and t=2. 1 f (2. 1) f (2)
